{"title":"外环面与内环面的力学差异","authors":"B. Sun, Guangming Song","doi":"10.1115/1.4062136","DOIUrl":null,"url":null,"abstract":"\n The formulation used by the most of studies on elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this paper, we will carry on author's previous work [B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of our own maple code, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus are the turning point of the Gaussion curvature at ϕ = 0, π, where the mechanics response of inner and outer torus is almost separated.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Mechanics Difference Between The Outer Torus and Inner Torus\",\"authors\":\"B. Sun, Guangming Song\",\"doi\":\"10.1115/1.4062136\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n The formulation used by the most of studies on elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this paper, we will carry on author's previous work [B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of our own maple code, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus are the turning point of the Gaussion curvature at ϕ = 0, π, where the mechanics response of inner and outer torus is almost separated.\",\"PeriodicalId\":54880,\"journal\":{\"name\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4062136\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4062136","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
The Mechanics Difference Between The Outer Torus and Inner Torus
The formulation used by the most of studies on elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this paper, we will carry on author's previous work [B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of our own maple code, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus are the turning point of the Gaussion curvature at ϕ = 0, π, where the mechanics response of inner and outer torus is almost separated.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation